Mathjax

General

Title	Formula	Markdown
Variables	$x_1$, $y_{\mathrm{0..}N}$ $z_{3,4}$	$x_1$, $z_{3,4}$
Square	$x_1$, $z_{3,4}$	$a^2$, $$x^y$, $2^{n-1}$
Square Root	$\sqrt{9}$, $\sqrt{x}$	$\sqrt{9}$, $\sqrt{x}$
Logarithm	$\log x$, ${\log }_{2}x$	$\log{}x$, $\log_{2}x$
Limits	${\lim }_{x\to \infty }$	$\lim_{x\to \infty}$
Fraction	$\frac{1}{2}$, ${\left(-\frac{1}{2}\right)}^n$	$\frac{1}{2}$, $\left(-\frac{1}{2}\right)^n$
Infinity	$\infty$	$infty$
Real numbers, Integers, Natural numbers, Rational numbers, Irrational numbers	$\mathbb{R}$, $\mathbb{Z}$, $\mathbb{N}$, $\mathbb{Q}$, $\mathbb{P}$	$\Bbb R$, $\Bbb Z$, $\Bbb N$, $\Bbb Q$, $\Bbb P$
Absolute Value	$|x|$, $|\frac{x}{2}|$, $\lfloor x\rfloor$, $\lceil x\rceil$	$\vert{x}\vert$, $\vert\frac{x}{2}\vert$, $\lfloor{x}\rfloor$, $\lceil{x}\rceil$
Arithmetic	$4+3$, $3-3$, $3\times 3$, $3÷3$	$4 + 3$, $3 - 3$, $3\times 3$, $3\div 3$
Factorial	$n!$	$n!$
Trigonometric functions	$\sin \theta$, $\cos \theta$, $\tan \theta$	$\sin\theta$, $\cos\theta$, $\tan\theta$
Greater or Less	$a>b$, $a\ge b$, $a<b$, $a\le b$	$a\gt b$, $a\geq b$, $a\lt b$, $a\leq b$
Much Less Than, Much Greater Than	$a\ll b$, $b\gg a$	$a \ll b$, $b \gg a$
Equation	$a=b$, $a\ne b$, $a\approx b$	$a=b$, $a\neq b$, $a\approx b$
Times Dot	$a\cdot b=ab$	$a\cdot b=ab$
Divide Fraction	$a/b=\frac{a}{b}$	$a/b=\frac{a}{b}$
Trinomial Equation	$a^2+b^2=c^2$	$a^2 + b^2 = c^2$
Matrix Parentheses	$\left(\begin{array}{cc}a& b\\ c& d\end{array}\right)$	$$\begin{pmatrix} a & b \\ c & d \end{pmatrix}$$
Matrix Brackets	$\left[\begin{array}{cc}a& b\\ c& d\end{array}\right]$	$$\begin{bmatrix} a & b \\ c & d \end{bmatrix}$$
Matrix Equation	$\left|\begin{array}{cc}a& b\\ c& d\end{array}\right|=ad-bc$	$$\begin{vmatrix} a & b \\ c & d \end{vmatrix}=ad-bc$$
Set	$x\in A$, $A\ni x$, $x\notin A$	$x\in A$, $A\ni x$, $x\notin A$
Subset	$A\subset B$, $A\subseteq B$, $A\not\subset B$	$A\subset B$, $A\subseteq B$, $A \not \subset B$
Intersection & Union	$A\cap B$, $A\cup B$, $\overline{A}$	$A\cap B$, $A\cup B$, $\overline{A}$
Logical Operators	$\forall X,\wedge X,\vee X,\neg X,\exists A,A⟹B$	$$ \forall X, \wedge X, \vee X, \neg X, \exists A A \implies B $$
Quadratic Formula	$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$	$x = {-b \pm \sqrt{b^2-4ac} \over 2a}$
Binomial	$\sqrt{3x-1}+(1+x{)}^2$	$\sqrt{3x-1}+(1+x)^2$
Differentiation	$f^{\prime }$, $f^{(n)}$, $D_{x}f$	$f'$, $f^{(n)}$, $D_x f$
Integral	${\int }_0^{1}f(x)dx$	$\int_0^1 f(x) dx$
Sigma	$\sum _{i=1}^k$	$\displaystyle \sum_{i=1}^k$
Integral Large	${\int }_{-\infty }^{\infty }f(x)dx$	$\displaystyle \int_{-\infty }^{\infty}f(x)dx$
Max Sample	$\max (a,b)=\{\begin{array}{ll}a& (a\geqq b)\\ b& (a<b)\end{array}$	$$\max(a,b)=\begin{cases}a&(a\geqq b)\\b&(a\lt b)\end{cases}$$
Piecewise Equations	$f(n)=\{\begin{array}{ll}n/2,& \text{if n is even}\\ 3n+1,& \text{if n is odd}\end{array}$	$$f(n) = \begin{cases} n/2, & \text{if $n$ is even} \\ 3n+1, & \text{if $n$ is odd} \end{cases}$$
Tables	$$\begin{array}{c	lcr} n & \text{Left} & \text{Center} & \text{Right} \ \hline 1 & 0.24 & 1 & 125 \ 2 & -1 & 189 & -8 \ 3 & -20 & 2000 & 1+10i \end{array}$$
Set Comprehensions	\{x \text{ if x is even} \mid x^2\in\Bbb Z\}	$\{x \text{ if $x$ is even} \mid x^2\in\Bbb Z\}$

Big O and Related Notations

Name	Running Time	Markdown
Big O [micron]	$0$ or $O$	$\mathcal{0}$ or $O$
Big Omega	$\Omega$	$\Omega$
Big Theta	$\Theta$	$\Theta$
Small O [micron]	$o$	$o$
Small Omega	$\omega$	$\omega$
On the order of	$\sim$	$\sim$

Common Time and Space Complexity

Name	Running Time	Markdown
Constant Time	$O(1)$	$O(1)$
Logarithmic Time	$O(\log n)$	$O(\log{}n)$
Linear Time	$O(n)$	$O(n)$
Quasilinear Time	$O(n\log n)$	$O(n\log{}n)$
Quadratic Time	$O(n^2)$	$O(n^2)$
Cubic Time	$O(n^3)$	$O(n^3)$
Factorial Time	$O(n!)$	$O(n!)$
Exponential Time	$O(2^n)$	$O(2^n)$